## Challenge

Define a function, TriangleType, that decides if a triangle is equilateral, isosceles, or scalene (or not a triangle at all). Your input will be three integers, each representing the measure of one interior angle. Your output should be “equilateral”, “isosceles”, “scalene”, or “not even a triangle”.

Original problem description on CEMC website.

Sample Output:

>>> TriangleType(70, 55, 55) "isosceles" >>> TriangleType(1,177,2) "scalene" >>> TriangleType(35,27,78) "not even a triangle"

## Background Information

Every triangle has the property that the sum of its interior angles is 180 degrees.

If all of the angles of a triangle are equal to each other (i.e., they all measure 60 degrees), then the triangle is called *equilateral*. If two of its angles are equal to each other, but the third is different, then the triangle is called *isosceles. *If all three angles are different, then the triangle is called *scalene*.

## Programming Tools (with Python examples)

**Defining a function.** The following example defines a function Sum which adds up three numbers a, b, and c.

def Sum(a,b,c): return a + b + c

Sample Output:

>>> Sum(1,2,3) 6 >>> Sum(-3,-1,4) 0 >>> Sum(3,4) ERROR (wrong number of inputs)

**Comparing two numbers.** It is often useful to compare two numbers using “less than,” “greater than,” “equal to,” “not equal to,” “less than or equal to,” “greater than or equal to.”

Sample Output:

>>> 1 < 2 True >>> 1 > 2 False >>> 1 != 2 True >>> 2 < 2 False >>> 2 <= 2 True >>> 2 >= 2 True >>> 2 == 2 True >>> 2 = 2 ERROR >>> Sum(1,2,3) == 6 True >>> Sum(0,1,1) != 2 False

**Basic flow control: If/then/else.** The following function decides whether a number is less than 100, between 100 and 1000, or more than 1000.

def HowBig(x): if x < 100: return "not that big." elif x < 1000: return "big." else: return "really big."

Sample Output:

>>> HowBig(3) "not that big." >>> HowBig(625.34) "big." >>> HowBig(123456789) "really big." >>> HowBig('apple') ERROR (must be a number to compare in lines 2 and 4)

## Extension

Let ABCD by a quadrilateral (four-sided polygon). Write a function to decide if ABCD is a parallelogram. The inputs of your function will be four integers, representing the measures of the angles, in clockwise order. Your output should be “parallelogram”, “not a parallelogram”, or “not even a quadrilateral”.